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I'm curious as to whether or not there is a method for solving higher-order systems of equations, for instance a system of a quadratic and two cubics in three variables, etc.
I'm doing some independent research on the topic and would like to know if any methods currently exist to solve such a system exactly--i.e., in terms of roots.
I acknowledge the fact that dimension-counting may result in the system being unsolvable beyond a certain extent--for instance, a system of three quadratics would probably be mathematically equivalent to the solutions of some sextic function which, unless factorable, would be impossible to solve exactly (unless some special application of Bring radicals were introduced).
Feedback, advice and links would be greatly appreciated.
I understand that numerical methods are much, much more efficient at tackling the problem of solving higher-order systems, but out of pure mathematical curiosity (of which I have much) I would like to attempt to solve them systematically and give a result in an exact form. If it proves mathematically necessary I can introduce Bring radicals into systems of sufficiently high total order. I have but one question: is this possible?
Thank you,
{?}--I also go by ?, Question Mark and QM
I'm doing some independent research on the topic and would like to know if any methods currently exist to solve such a system exactly--i.e., in terms of roots.
I acknowledge the fact that dimension-counting may result in the system being unsolvable beyond a certain extent--for instance, a system of three quadratics would probably be mathematically equivalent to the solutions of some sextic function which, unless factorable, would be impossible to solve exactly (unless some special application of Bring radicals were introduced).
Feedback, advice and links would be greatly appreciated.
I understand that numerical methods are much, much more efficient at tackling the problem of solving higher-order systems, but out of pure mathematical curiosity (of which I have much) I would like to attempt to solve them systematically and give a result in an exact form. If it proves mathematically necessary I can introduce Bring radicals into systems of sufficiently high total order. I have but one question: is this possible?
Thank you,
{?}--I also go by ?, Question Mark and QM
